Abstract: This Letter presents evidence for single top-quark production in the s-channel using proton-proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS detector at the CERN Large Hadron Collider. The analysis is performed on events containing one isolated electron or muon, large missing transverse momentum and exactly two b-tagged jets in the final state. The analysed data set corresponds to an integrated luminosity of 20.3 fb(-1). The signal is extracted using a maximum-likelihood fit of a discriminant which is based on the matrix element method and optimized in order to separate single-top-quark s-channel events from the main background contributions, which are top-quark pair production and W boson production in association with heavy-flavour jets. The measurement leads to an observed signal significance of 3.2 standard deviations and a measured cross-section of sigma s = 4.8 +/- 0.8(stat.)(-1.3)(+1.6)(syst.) pb, which is consistent with the Standard Model expectation. The expected significance for the analysis is 3.9 standard deviations.